Supposean converges conditionally (but not absolutely). Let A+ = {n €N : an ≥ 0} n=0 and A_ = {n € N : an <0}. Prove that nEA+ an and Σ an diverge. nЄA_

Q: (b) Let a1 = 1 and an+1 = lim, an- /am+2. Prove that a, is convergent and find %3D

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: Show the following statement is true or not with proof. If {n} converges then {[sn]} converges.

A: We have to show the following statement is true or not with proof. If {sn} converges then {|sn|}…

Q: H.w.Which af the fallowing series converge or diverg 80 Ln n 2. (h+i)! hai 4- n+4

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A: The objective of the question is checking the convergence or divergence of the given series.

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Q: 1+ 1 + 1 V 3 + 1 43 Select one: Qa converges O b. It is inconclusive O c. diverges +...

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Q: Ean converges and an > 0 for all n , can anything be said about E? An

A: If ∑ an converges and an &gt; 0 for all n then ∑ 1an  converges         Proof :…

Q: 3. Prove that if E has finite measure and let {f.}be a sequence of measurable functions on E that…

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Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

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Q: 4 Suppose that lim anti n7708 an =P -=p. For which values of P must Σ2" an converge?

A: To determine the values of p  for which the series ∑n=1∞​2nan​  converges, we can use the given…

Q: w/ バ+n 3n't -5- an- anD 70+4n? 3n-1

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Q: 21.) Converge or diverge? Explain. En=1 3n - п!

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Q: Let x be the sequence X 1, 2, 3, Select ALL of the correct statements (note that there may be more…

A: Note the following properties about sequence and subsequence : Every subsequence of convergent…

Q: Write TRUE if the statement is always correct and FALSE if otherwise. Prove your answer. (a) If an…

A: The given statement is (a) If an≥0 for all n∈ℕ, then ∑n=1∞an does not converge conditionally.…

Q: Exercise 1. Let an 2n 3n+ 1 (a) Determine whether (an) is convergent. (b) Determine whether an is…

A: Part (a) A sequence an is said to be convergent if limn→∞an exists and is finite. Determine limn→∞an…

Q: (-1)* k4/3 k=1 a) Converges both absolutely and conditionally b) Converges conditionally c)…

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Q: Σ (-1)* converges. Vk Determine whether k=1

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Q: Do these converge, (absolutely, Conditionally) or diverge ¹){( n=1 2.) 8 WE 2n+3 35n+1 3.). 8Wä 4.)…

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Q: i) Let {n} a sequence of non-negative terms that is monotone decreasing and în → 0. If SnX1 X2 + x3…

A: Given that, { xn } is a sequence of non negative terms and this sequence is monotonic decreasing,…

Q: Show that if lim 0 and E- b, converges then Ena, a, converges too.

A: We have to Prove that series an is convergent.

Q: Fend the Rmit of the following aq =2 %3D a2=12-52 %3D 2-2+2+2+ ... + U.

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Q: تفاضل وتكامل )2( نظري 1 If pconverges, then p could be xP to Select one: а. 3/2 stion 1 b. 1 Oc. non…

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Q: h reason or proof whether each of the fo ents of a sequence of random variables {-

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Q: Let an 6n 2n + 1 (a) Determine whether {a} is convergent. O convergent divergent = (b) Determine…

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Q: Show that a, converges to A iff {a, - A) converges to 0.

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Q: Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²).…

A: Given equality: ∑i=0nxi·∑i=0nyi=∑i=0nxiyi   a) Verify the equality is always true. If not, give an…